The perimeter of a circular lawn is 1232 m. There is 7 m wide path around the lawn. The area (in m$$^2$$) of the path is:(Take $$\pi = \frac{22}{7}$$)

Let the radius of the circular lawn = r

The perimeter of a circular lawn is 1232 m.

$$2\times\frac{22}{7}\times r=1232$$

r = 196 m

Area of the path = $$\pi\left(r+7\right)^2-\pi\ r^2$$

= $$\frac{22}{7}\left[\left(r+7\right)^2-r^2\right]$$

= $$\frac{22}{7}\left[\left(196+7\right)^2-196^2\right]$$

= $$\frac{22}{7}\left[203^2-196^2\right]$$

= $$\frac{22}{7}\left[\left(203+196\right)\left(203-196\right)\right]$$

= $$\frac{22}{7}\left[\left(399\right)\left(7\right)\right]$$

= 8778 m$$^2$$

Hence, the correct answer is Option A